Last we heard from director Clint Eastwood, he was fumbling his way through the adaptation of the jukebox musical Jersey Boys. So naturally he would quickly follow that up with American Sniper, a modern warfare movie tackling the story of Chris Kyle, who was considered the deadliest sniper in U.S. history.

Kyle (Bradley Cooper) was a Texas native whose dreams of being a cowboy took a back seat when he saw attacks on the U.S. around the world, including on 9/11. Recruited to be a Navy SEAL, he ended up serving four tours of duty in Iraq, coming to be known far and wide on both sides of the war for his proficiency with a long-range rifle.

Using a Texas drawl and a clinched jaw, Bradley Cooper makes Kyle into a man’s man who also understands his limitations.

Eastwood and screenwriter Jason Hall worked from Kyle’s own book; they had only just begun when Kyle was shot and killed at a North Texas gun range in February 2013. They attempt to give a full sense of the man, devoting significant portions to Kyle’s home life — or perhaps lack thereof — with his wife, Taya (Sienna Miller). They show Kyle to be a man who’s torn between his sense of duty to his country and his obligation to his family at home.

Eastwood, who did a great job with the World War II double feature Flags of Our Fathers and Letters from Iwo Jima, takes on a different animal with this film. Even now, what the military had to face during the war with Iraq started under President George W. Bush is difficult to understand completely, so working up enmity toward the opposition in a film is equally challenging.

That doesn’t stop Eastwood from trying, as he makes much of an enemy sniper who was just as fearsome as Kyle. That foe, multiple moral quandaries and other decisions most of us would never want to face are what Kyle had to deal with during his time in Iraq, and for the most part Eastwood and Hall do a solid job in making them as dramatic as possible.

Still, the film could have used a bit more subtlety. The combat scenes often hark back to old-style war films where the killing of the enemy, rather than strategy, is the only thing that mattered. And Kyle’s time at home in between tours feels rushed, so the audience never fully comes to grips with what he is feeling.

Cooper plays Kyle with a sensitivity that belies his bulked-up appearance. Using a Texas drawl and a clinched jaw, he makes Kyle into a man’s man who also understands his limitations. Miller is a chameleon who also hid in plain sight in Foxcatcher. She is a great complement to Cooper, turning a possibly one-note role into something much richer.

Unlike films like The Hurt Locker or Zero Dark Thirty, there are few big lessons to learn from American Sniper. But as a tribute to a soldier whom many others credit with saving their lives, it more than fits the bill.